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Intervals in the Hales-Jewett theorem

Conlon, David and Kamčev, Nina (2018) Intervals in the Hales-Jewett theorem. . (Unpublished)

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The Hales-Jewett theorem states that for any m and r there exists an n such that any r-colouring of the elements of [m]^n contains a monochromatic combinatorial line. We study the structure of the wildcard set S ⊆ [n] which determines this monochromatic line, showing that when r is odd there are r-colourings of [3]^n where the wildcard set of a monochromatic line cannot be the union of fewer than r intervals. This is tight, as for n sufficiently large there are always monochromatic lines whose wildcard set is the union of at most r intervals.

Item Type:Report or Paper (Discussion Paper)
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URLURL TypeDescription Paper
Conlon, David0000-0001-5899-1829
Additional Information:Conlon research supported by a Royal Society University Research Fellowship and by ERC Starting Grant 676632. The second author would like to thank Sarah Gales, Hannah and Sven Eggimann for hosting her in Oxford while this research was conducted. We would also like to thank the anonymous referee for a number of helpful remarks.
Funding AgencyGrant Number
European Research Council (ERC)676632
Record Number:CaltechAUTHORS:20190819-170911002
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:98026
Deposited By: Melissa Ray
Deposited On:20 Aug 2019 19:50
Last Modified:03 Oct 2019 21:37

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